Does the body not clear drugs like caffeine at a constant rate? If you drink less caffeine does the body clear it less quickly? Or am I not understanding it? Caffeine half life is about 5 hours (via Google), so regardless of if I drink 100mg or 900mg of caffeine, half (50mg or 450mg) will be left in my body 5 hours later? That seems like a pretty drastic difference in the rate of clearance.
In: 509
Think about your liver and kidneys like the filtration system for a swimming pool. It processes a certain amount of fluid in a given time.
Suppose you dumped a bunch of dirt into a swimming pool all at once and mixed it up so it had a uniform concentration. When the filter processes a liter of water, it dumps the cleaner
water back into the pool, so the entire pool is a little bit cleaner. Now the next liter of water has a lower concentration of dirt, so the filter removes less total dirt the second time. Then the pool is slightly cleaner, and the third liter of water has less dirt… and so on.
Mathematically, this means that the rate at which dirt is removed is proportional to the total amount of dirt in the pool. (If you assume that the water has an efficient mixer so there aren’t clean regions and dirty regions of the pool.) The solution to an equation like that is exponential.
C(t) = C(0) * exp(-kt)
where C(t) is the concentration of dirt over time, and
k is called the decay constant (relates to how fast the filter can remove dirt)
Because exp(ln(2)) = 2, we can write the above equation more like
C(t) = C(0) * (1/2) ^ (t/H)
Where H is the half-life.
You can use a little algebra to see how k and H are related: k = ln(2) / H
Latest Answers